Conversations on Mind, Matter, and Mathematics

Overview

In a wide-ranging series of conversations Jean-Pierre Changeux and Alain Connes discuss the development of the human brain as a function of natural selection and variation, debate the character of human intelligence (and the obstacles that stand in the way of simulating, modeling, or actually reproducing it by mechanical means), dispute the reasons for the "unreasonable effectiveness" of mathematics in explaining the physical world, and differ over the sources of mathematical creativity. In an epilogue they go on...
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Overview

In a wide-ranging series of conversations Jean-Pierre Changeux and Alain Connes discuss the development of the human brain as a function of natural selection and variation, debate the character of human intelligence (and the obstacles that stand in the way of simulating, modeling, or actually reproducing it by mechanical means), dispute the reasons for the "unreasonable effectiveness" of mathematics in explaining the physical world, and differ over the sources of mathematical creativity. In an epilogue they go on to inquire into the relation of mathematics and science to ethics, asking whether a code of human morality consistent with what is known about the structure and function of the human brain can be devised, and whether the "enlargement of human sympathies" hoped for by Darwin, Kropotkin, and others may be given a natural basis. This vivid record of profound disagreement, and, at the same time, passionate search for mutual understanding, follows in the modern tradition of Poincare, Turing, Hadamard, and von Neumann in probing the limits of human rationality and intellectual possibility. Why order should exist in the world at all - and why it should be comprehensible by human beings - is the question that lies at the heart of these remarkable dialogues.
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Editorial Reviews

Brenda Grazis
An intriguing argument by mathematician Connes in this spirited conversation with neurobiologist Changeux is that a mathematical reality exists independently of the human mind. For example, he considers it improbable that the cosmic harmony of the Jovian satellites orbiting in consonance with Kepler's laws is a product of the human brain. Thus, although an understanding of the brain as a tool may lead to expanded knowledge, Connes denies that such understanding will alter mathematical reality. However, Changeux believes that the concept of an immutable mathematical reality is merely "the fascination that the created object exerts upon its creator," and he rejects the idea that a "totally organized mathematical system exists in nature waiting to be gradually discovered." Among various other fascinating ideas discussed is the role of the brain's limbic system in cognition, such as how the emotions aroused by a pleasurable hypothesis may serve as a guide to a solution.
New York Times Book Review
A stimulating and illuminating book. . . . Mr. Changeux and Mr. Connes might best be characterized by reviving an old term. They are natural philosophers, concerned with large questions about the world and our place in it, who confront those questions with intelligence and lively imagination.
— Philip Kitcher
Choice
A highly entertaining and erudite read, this conversation between two renowned scientists . . . is at all times informative, lively, and thought provoking. The reader is drawn into the argument and left pondering the issues well after the last page has been turned.
Nature
A delight to read, and highly informative.
— Keith Devlin
Times Literary Supplement
The record of an intellectual encounter between two of Franco's leading scientific figures. . . . The result is a smooth, easy-to-read representation of a protracted, interesting . . . exchange between Alain Connes, an eminent mathematician, . . . and Jean-Pierre Changeux, a distinguished biologist. . . .
— Brian Rotman
The New York Times Book Review
[The authors'] passion for discerning the truth about important issues and for formulating thoughts as precisely as possible shines through these conversations.... A stimulating and illuminating book.
— Philip Kitcher
The Times Higher Education Supplement
The original Socratic dialogues were artificially constructed to present a coherent view. The dialogue between Connes and Changeux is quite different. It is the recording of real-life arguments where the speakers are frequently at cross-purposes and operate in different planes. For the reader this can be irritating but it also encourages him to become involved and frame his own answers. . . .
— Sir Michael Atiyah
The New York Times Book Review - Philip Kitcher
A stimulating and illuminating book. . . . Mr. Changeux and Mr. Connes might best be characterized by reviving an old term. They are natural philosophers, concerned with large questions about the world and our place in it, who confront those questions with intelligence and lively imagination.
Sir; The Times Higher Education Supplement - Michael Atiyah
The original Socratic dialogues were artificially constructed to present a coherent view. The dialogue between Connes and Changeux is quite different. It is the recording of real-life arguments where the speakers are frequently at cross-purposes and operate in different planes. For the reader this can be irritating but it also encourages him to become involved and frame his own answers. . . .
Nature - Keith Devlin
A delight to read, and highly informative.
Times Literary Supplement - Brian Rotman
The record of an intellectual encounter between two of Franco's leading scientific figures. . . . The result is a smooth, easy-to-read representation of a protracted, interesting . . . exchange between Alain Connes, an eminent mathematician, . . . and Jean-Pierre Changeux, a distinguished biologist. . . .
The Times Higher Education Supplement - Sir Michael Atiyah
The original Socratic dialogues were artificially constructed to present a coherent view. The dialogue between Connes and Changeux is quite different. It is the recording of real-life arguments where the speakers are frequently at cross-purposes and operate in different planes. For the reader this can be irritating but it also encourages him to become involved and frame his own answers. . . .
From the Publisher
One of Choice's Outstanding Academic Titles for 1995

"[The authors'] passion for discerning the truth about important issues and for formulating thoughts as precisely as possible shines through these conversations.... A stimulating and illuminating book."—Philip Kitcher, The New York Times Book Review

"A stimulating and illuminating book. . . . Mr. Changeux and Mr. Connes might best be characterized by reviving an old term. They are natural philosophers, concerned with large questions about the world and our place in it, who confront those questions with intelligence and lively imagination."—Philip Kitcher, New York Times Book Review

"The original Socratic dialogues were artificially constructed to present a coherent view. The dialogue between Connes and Changeux is quite different. It is the recording of real-life arguments where the speakers are frequently at cross-purposes and operate in different planes. For the reader this can be irritating but it also encourages him to become involved and frame his own answers. . . . "—Sir Michael Atiyah, The Times Higher Education Supplement

"A highly entertaining and erudite read, this conversation between two renowned scientists . . . is at all times informative, lively, and thought provoking. The reader is drawn into the argument and left pondering the issues well after the last page has been turned."—Choice

"A delight to read, and highly informative."—Keith Devlin, Nature

"The record of an intellectual encounter between two of Franco's leading scientific figures. . . . The result is a smooth, easy-to-read representation of a protracted, interesting . . . exchange between Alain Connes, an eminent mathematician, . . . and Jean-Pierre Changeux, a distinguished biologist. . . ."—Brian Rotman, Times Literary Supplement

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Product Details

  • ISBN-13: 9780691087597
  • Publisher: Princeton University Press
  • Publication date: 4/17/1995
  • Edition number: 1
  • Pages: 240
  • Product dimensions: 5.89 (w) x 8.87 (h) x 0.94 (d)

Table of Contents

Translator's Note
Preface to the Original French Edition
1 Mathematics and the Brain 3
2 Plato as Materialist? 25
3 Nature Made to Order 41
4 The Neuronal Mathematician 74
5 Darwin among the Mathematicians 122
6 Thinking Machines 153
7 The Real and the Rational 179
Epilogue: Ethical Questions 210
Glossary of Mathematical Terms 237
Glossary of Neurobiological Terms 247
Index 253
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